"""simple docstring"""


from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch


@dataclass
class 							a					:
    _snake_case  :	List[Any]  				=				42  # [batch_size x 3]
    _snake_case  :	int  				=				42  # [batch_size x 3]
    _snake_case  :	List[str]  				=				42  # [batch_size x 3]
    _snake_case  :	Optional[int]  				=				42  # [batch_size x 3]
    _snake_case  :	Optional[Any]  				=				42
    _snake_case  :	Any  				=				42
    _snake_case  :	Dict  				=				42
    _snake_case  :	str  				=				42
    _snake_case  :	Tuple  				=				42


    def   lowerCAmelCase_	(       self						:	Optional[int]       ):
      assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
      assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
      assert len(self.x.shape       ) == len(self.y.shape       ) == len(self.z.shape       ) == len(self.origin.shape       ) == 2


    def   lowerCAmelCase_	(       self						:	int       ):
      return torch.from_numpy(np.array([self.width, self.height] ,					dtype=np.floataa       )       )


    def   lowerCAmelCase_	(       self						:	Dict       ):
      return torch.from_numpy(np.array([self.x_fov, self.y_fov] ,					dtype=np.floataa       )       )


    def   lowerCAmelCase_	(       self						:	List[str]       ):
      _UpperCAmelCase    			=   torch.arange(self.height * self.width       )
      _UpperCAmelCase    			=   torch.stack(
          [
              pixel_indices % self.width,
              torch.div(__snake_case ,					self.width ,					rounding_mode="""trunc"""       ),
          ] ,					axis=1 ,					)
      return coords


    @property
    def   lowerCAmelCase_	(       self						:	str       ):
      _UpperCAmelCase    			=   self.shape
      _UpperCAmelCase    			=   int(np.prod(__snake_case       )       )

      _UpperCAmelCase    			=   self.get_image_coords()
      _UpperCAmelCase    			=   torch.broadcast_to(coords.unsqueeze(0       ) ,					[batch_size * inner_batch_size, *coords.shape]       )
      _UpperCAmelCase    			=   self.get_camera_rays(__snake_case       )

      _UpperCAmelCase    			=   rays.view(__snake_case ,					inner_batch_size * self.height * self.width ,					2 ,					3       )

      return rays


    def   lowerCAmelCase_	(       self						:	Union[str, Any] ,					__lowerCAmelCase						:	torch.Tensor       ):
      _UpperCAmelCase    			=   coords.shape
      assert n_coords == 2
      assert batch_size == self.origin.shape[0]

      _UpperCAmelCase    			=   coords.view(__snake_case ,					-1 ,					2       )

      _UpperCAmelCase    			=   self.resolution()
      _UpperCAmelCase    			=   self.fov()

      _UpperCAmelCase    			=   (flat.float() / (res - 1)) * 2 - 1
      _UpperCAmelCase    			=   fracs * torch.tan(fov / 2       )

      _UpperCAmelCase    			=   fracs.view(__snake_case ,					-1 ,					2       )
      _UpperCAmelCase    			=   (
          self.z.view(__snake_case ,					1 ,					3       )
          + self.x.view(__snake_case ,					1 ,					3       ) * fracs[:, :, :1]
          + self.y.view(__snake_case ,					1 ,					3       ) * fracs[:, :, 1:]
      )
      _UpperCAmelCase    			=   directions / directions.norm(dim=-1 ,					keepdim=__snake_case       )
      _UpperCAmelCase    			=   torch.stack(
          [
              torch.broadcast_to(self.origin.view(__snake_case ,					1 ,					3       ) ,					[batch_size, directions.shape[1], 3]       ),
              directions,
          ] ,					dim=2 ,					)
      return rays.view(__snake_case ,					*__snake_case ,					2 ,					3       )


    def   lowerCAmelCase_	(       self						:	Any ,					__lowerCAmelCase						:	int ,					__lowerCAmelCase						:	int       ):
      assert width * self.height == height * self.width, "The aspect ratio should not change."
      return DifferentiableProjectiveCamera(
          origin=self.origin ,					x=self.x ,					y=self.y ,					z=self.z ,					width=__snake_case ,					height=__snake_case ,					x_fov=self.x_fov ,					y_fov=self.y_fov ,					)






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   []
  for theta in np.linspace(0 ,2 * np.pi ,num=20		):
    _UpperCAmelCase    			=   np.array([np.sin(_A		), np.cos(_A		), -0.5]		)
    z /= np.sqrt(np.sum(z**2		)		)
    _UpperCAmelCase    			=   -z * 4
    _UpperCAmelCase    			=   np.array([np.cos(_A		), -np.sin(_A		), 0.0]		)
    _UpperCAmelCase    			=   np.cross(_A ,_A		)
    origins.append(_A		)
    xs.append(_A		)
    ys.append(_A		)
    zs.append(_A		)
  return DifferentiableProjectiveCamera(
      origin=torch.from_numpy(np.stack(_A ,axis=0		)		).float() ,x=torch.from_numpy(np.stack(_A ,axis=0		)		).float() ,y=torch.from_numpy(np.stack(_A ,axis=0		)		).float() ,z=torch.from_numpy(np.stack(_A ,axis=0		)		).float() ,width=_A ,height=_A ,x_fov=0.7 ,y_fov=0.7 ,shape=(1, len(_A		)) ,)





'''simple docstring'''






from __future__ import annotations
def  lowerCamelCase__			(		_A					,     _A					,     _A							):
  a		:   List[str]	  =	list(range(len(_A							)							)							)
  a		:   Union[str, Any]	  =	[v / w for v, w in zip(_A					,     _A							)]
  index.sort(key=lambda _A							: ratio[i]					,     reverse=_A							)

  a		:   float	  =	0
  a		:   list[float]	  =	[0] * len(_A							)
  for i in index:
    if weight[i] <= capacity:
      a		:   int	  =	1
      max_value += value[i]
      capacity -= weight[i]
    else:
      a		:   Optional[int]	  =	capacity / weight[i]
      max_value += value[i] * capacity / weight[i]
      break

  return max_value, fractions


if __name__ == "__main__":
     import doctest

     doctest.testmod()